Math 4045/5045: Advanced Algebra I

Fall 2017, Dalhousie University

Time and location: Mondays, Wednesdays & Fridays 11:35--12:25 pm in Chase 227.


Office hours: Tuesdays 10--11 am & Wednesdays 1:30--2:30 pm in Chase 314.


Course Syllabus: can be found here.



Homework: Homework:

Homework Problems Due Date
HW#1 Chapter III Section 2: 13, 18, 21; Chapter IV Section 1: 2, 3 Wednesday Sept 20
HW#2 Chapter IV Section 1: Write proofs for theorems 1.11, 1.12, 1.13; Exercises: 4, 13 Wednesday Sept 27
HW#3 Chapter IV Section 2: 1, 4, 7 Wednesday Oct 4
HW#4 Chapter IV Section 1: 11; Section 2: 2.10, 2.12; Section 6: 6.2, 6.4; Wednesday Oct 18
HW#5 Chapter IV Prove Proposition 3.7 and do Section 3: 2, 5, 6, 9, 12 Wednesday Nov 15


Calendar:

Date Topics Covered
W Sep 6 Reviewed rings and ideals (Chapter III)
F Sep 8 Definitions of categories, modules and submodules
M Sep 11 Homomorphisms, Hom, and quotient modules
W Sep 13 Module Isomorphism Theorems
F Sep 15 Generators of modules
M Sep 18 Exact Sequences
W Sep 20 Split exact sequences
F Sep 22 Free modules
M Sep 25 More on free modules
W Sep 27 vector spaces: free modules over division rings
F Sep 29 Started discussin on rank
M Oct 2 Rank of free modules over division rings
W Oct 4 Invariant rank property
F Oct 6 Noetherian modules, Torsion modules
M Oct 9 THANKSGIVING-- NO CLASS
W Oct 11 Modules over PIDs
F Oct 13 Modules over PIDs
M Oct 16 Modules over PIDs
W Oct 18 Modules over PIDs
F Oct 20 Modules over PIDs
M Oct 23 MIDTERM
W Oct 25 Projective modules
F Oct 27 Projective modules and injective modules
M Oct 30 Baer's criterion and divisible modules
T Oct 31[LAST DAY TO DROP WITH W] NO CLASS
W Nov 1 Injective modules
F Nov 3 Every module over a ring with identity is contained in an injective one
M Nov 6 STUDY BREAK -- NO CLASS
W Nov 8 STUDY BREAK -- NO CLASS
F Nov 10 STUDY BREAK -- NO CLASS
M Nov 13 REMEMBRANCE DAY -- NO CLASS
W Nov 15 Hom is left exact
F Nov 17 Special cases when Hom is also right exact; bimodules
M Nov 20
W Nov 22
F Nov 24
M Nov 27
W Nov 29
F Dec 1
M Dec 4
T Dec 5 LAST DAY -- MONDAY SCHEDULE